They attributed this to the early onset of diffuser stall observed for these non-uniform inflows due to the accentuation of the flow profile. They found that these non-uniform inflows resulted in poorer diffuser performance than for a uniform inflow. For each case, they studied straight sided diffusers with linearly expanding walls, using several different expansion angles and non-dimensional lengths. They considered an asymmetric flow profile with uniform shear, an asymmetric step-shear profile, a symmetric jet profile, and a symmetric wake profile. The experiments of Wolf and Johnston studied several non-uniform inlet flows for a two-dimensional diffuser. They found that both of these non-uniform flow profiles became accentuated by the diffuser. Horlock and Lewis studied an asymmetric shear flow and a symmetric wake flow in a linearly expanding two-dimensional diffuser using a simple inviscid model and experiments. In the case where the inflow is non-uniform, there have been some experimental studies which have investigated diffuser performance for specific inflow profiles. The optimum angle varies slightly, depending on the inflow boundary layer thickness, and whether the diffuser is two-dimensional or axisymmetric. The optimal angle strikes a balance between not being too shallow, since thin channels have larger wall drag, and not being too wide, since wide expansion angles result in boundary layer separation and poor consequent pressure recovery. In the case where the inflow is uniform, diffusers are usually designed to be straight sided, and the expansion angle is critical to performance. There is a large body of literature on diffusers in the case where the inflow is uniform (see ), but only a limited literature available for non-uniform inlet flows. Diffusers have numerous applications, from turbines in aerospace to hydropower to automotive design. Expanding channels, known as diffusers, have the function of converting high-speed low-pressure flow to low-speed high-pressure flow.

In this study, we consider a class of expanding channel flows in which the inflow is non-uniform. This suggests a low-dimensional parameterisation of the shapes, providing a structure in which more detailed and computationally expensive turbulence models can be used to find optimal shapes for more realistic flow behaviour. We show that some of the optimal diffuser shapes can be well approximated by piecewise linear sections. A numerical optimisation approach is used to solve the optimal control problem and PontryaginвЂ™s maximum principle is used to find analytical solutions in the second and third cases. The governing equations of this model form the dynamics of an optimal control problem where the control is the diffuser channel shape. The model consists of integrated mass and momentum equations, where wall drag is treated with a friction factor parameterisation.

We describe the evolution of the time-averaged flow profile using a reduced mathematical model that has been previously tested against experiments and computational fluid dynamics models. The third case is a pure shear profile with linear velocity variation between the centre and outer edge of the diffuser. The second case is a limiting case when these streams are of similar speed. The first case has inner and outer streams of different speeds, with a velocity jump between them that evolves into a shear layer downstream. Three classes of non-uniform inflow are considered, with the axial velocity varying across the width of the diffuser entrance. We find that optimal diffuser shapes strike a balance between not widening too soon, as this accentuates the non-uniform flow, and not staying narrow for too long, which is detrimental for wall drag. A simplified model is used to identify the diffuser shape that maximises pressure recovery for several classes of non-uniform inflow.

Sharp driver optimal control model